The main goal of this project is to develop a general statistical theory for making inferences about the gene order on a chromosome. Besides its theoretical relevance, it leads to important practical applications: the construction of the human gene map and the improvement of the accuracy of genetic counseling and prenatal diagnosis. We aim at developing optimal decision procedures to order an arbitrarily high number of genes. This will be accomplished by constructing multiple-step decision procedures (procedures where multiple nonindependent tests are performed to order overlapping sequences of genes). Since one-step procedures (procedures where all the hypotheses are considered simultaneously) are repeatedly used in multiple-step procedures, we shall derive efficient one-step procedures. To develop optimal one- and multiple-step procedures we shall consider different statistical approaches (classical Bayes, empirical Bayes and generalized likelihood), sampling schemes (fixed sample size, sequential, and group sequential), genetic models (recombination fractions, map distances, misclassification parameters, incomplete penetrance), and sources of genetic information (phase-known backcross system and generic pedigree structure). The key feature of the ordering procedures we shall develop is to control the probability of committing decision errors. The second goal of this project is to develop a general statistical theory for estimating the genetic risk and to evaluate how the uncertainty on the gene order and genetic distances reflects on the precision of genetic risks estimates, used in genetic counseling. The statistical methods will be implemented in computer programs and evaluated with simulated and real data.